The investor problem based on the HJM model

Szymon Peszat¹ ; Dariusz Zawisza¹

¹ Faculty of Mathematics and Computer Science Jagiellonian University Łojasiewicza 6 30-348 Kraków, Poland

Annales Polonici Mathematici, Tome 127 (2021) no. 3, pp. 241-269

Résumé

We consider a consumption-investment problem (both on a finite and an infinite time horizon) in which the investor has access to a bond market. In our approach prices of bonds with different maturities are described by the general HJM factor model. We assume that the bond market consists of the whole family of rolling bonds and the investment strategy is a general signed measure distributed on all real numbers representing time to maturity specifications for different rolling bonds. In particular, we can consider a portfolio of coupon bonds. The investor’s objective is to maximize the time-additive HARA utility of the consumption process. We solve the problem by means of the HJB equation for which we prove the required regularity of solution and all required estimates to ensure applicability of the verification theorem. Explicit calculations for affine models are presented.

Détail

DOI : 10.4064/ap210429-12-11

Keywords: consider consumption investment problem finite infinite time horizon which investor has access bond market approach prices bonds different maturities described general hjm factor model assume bond market consists whole family rolling bonds investment strategy general signed measure distributed real numbers representing time maturity specifications different rolling bonds particular consider portfolio coupon bonds investor objective maximize time additive hara utility consumption process solve problem means hjb equation which prove required regularity solution required estimates ensure applicability verification theorem explicit calculations affine models presented